# Crystal truncation rods from miscut surfaces

## TL;DR

This paper develops a model to analyze how miscut surfaces with steps and terraces affect crystal truncation rods, providing insights into surface roughness and morphology characterization.

## Contribution

The paper introduces a new model for crystal truncation rods from miscut surfaces, accounting for non-uniform terraces and jagged steps, validated with SrTiO3 samples.

## Key findings

- Non-uniform terrace widths decrease rod intensity.
- Jagged step edges reduce scattering intensity.
- Model accurately characterizes surface roughness.

## Abstract

Crystal truncation rods are used to study surface and interface structure. Since real surfaces are always somewhat miscut from a low index plane, it is important to study the effect of miscut on crystal truncation rods. We develop a model that describes the truncation rod scattering from miscut surfaces that have steps and terraces. We show that non-uniform terrace widths and jagged step edges are both forms of roughness that decrease the intensity of the rods. Non-uniform terrace widths also result in a broad peak that overlaps the rods. We use our model to characterize the terrace width distribution and step edge jaggedness on three SrTiO$_3$ (001) samples, showing excellent agreement between the model and the data, confirmed by atomic force micrographs of the surface morphology. We expect our description of terrace roughness will apply to many surfaces, even those without obvious terracing.